Page 34 - Statistics and Data Analysis in Geology

Elementary Statistics

The probability of making x discoveries in a drilling program of n holes, when
sampling from a population of N prospects of which S are believed to contain
reservoirs, is

This is the number of combinations of the reservoirs taken by the number of discov-
eries, times the number of combinations of barren anomalies taken by the number
of dry holes, all divided by the number of combinations of all the prospects taken
by the total number of holes in the drilling program.
The hypergeometric probability distribution can be applied to our offshore
concession that contains ten seismic features, of which four are likely to be struc-
tures containing reservoirs. Unfortunately, we cannot know in advance of drilling
which four of the ten features will prove productive. If the current season’s explo-
ration budget permits the drilling of only four of the prospects, we can determine
the probabilities attached to the various possible outcomes.
What is the probability that the drilling program will be a total failure, with no
discoveries among the four features tested?

The probability of gambler’s ruin is approximately 7%. What is the probability that
one discovery will be made?

The probability that one discovery will be made is 38%.
A histogram can be prepared which shows the probabilities attached to all
possible outcomes in this exploration situation (Fig. 2-7). Note that the probability
of some success is (1.00 - 0.07), or 93%.
The preceding examples have addressed situations where there are only two
possible outcomes: a hole is dry, or oil is discovered. If oil is found, the well cannot
be dry, and vice versa. Events in which the occurrence of one outcome precludes the
occurrence of the other outcome are said to be mutually exclusive. The probability
that one event or the other happens is the sum of their separate probabilities; that
is, p (discovery or dry hole) = p (discovery) + p (dry hole). This is called the additive
rule of probability.
Events are not necessarily mutually exclusive. For example, we may be drilling
an exploratory hole for oil or gas in anticipation of hitting a porous reservoir sand-
stone in what we have interpreted as an anticlinal structure from seismic data. The

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